1. **State the problem:** Solve the system of equations using substitution method: $$2x + y = 7$$ $$x - 3y = 14$$ 2. **Isolate one variable:** From the first equation, solve for $y$: $$y = 7 - 2x$$ 3. **Substitute into second equation:** Replace $y$ in the second equation with $7 - 2x$: $$x - 3(7 - 2x) = 14$$ 4. **Simplify and solve for $x$:** $$x - 21 + 6x = 14$$ $$7x - 21 = 14$$ $$7x = 14 + 21$$ $$7x = 35$$ $$x = \frac{35}{7}$$ $$x = 5$$ 5. **Substitute $x=5$ back to find $y$:** $$y = 7 - 2(5)$$ $$y = 7 - 10$$ $$y = -3$$ 6. **Solution:** The solution to the system is $\boxed{(5, -3)}$ which corresponds to option B. This means the lines intersect at the point $(5, -3)$.